stzrzf (3p)

Name

stzrzf - N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations

Synopsis

SUBROUTINE STZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)

INTEGER M, N, LDA, LWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)

SUBROUTINE STZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)

INTEGER*8 M, N, LDA, LWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)




F95 INTERFACE
SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)

INTEGER :: M, N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A

SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)

INTEGER(8) :: M, N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A




C INTERFACE
#include <sunperf.h>

void stzrzf(int m, int n, float *a, int lda, float *tau, int *info);

void stzrzf_64(long m, long n, float *a, long  lda,  float  *tau,  long
*info);

Description

Oracle Solaris Studio Performance Library                           stzrzf(3P)



NAME
       stzrzf  - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to
       upper triangular form by means of orthogonal transformations


SYNOPSIS
       SUBROUTINE STZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)

       INTEGER M, N, LDA, LWORK, INFO
       REAL A(LDA,*), TAU(*), WORK(*)

       SUBROUTINE STZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)

       INTEGER*8 M, N, LDA, LWORK, INFO
       REAL A(LDA,*), TAU(*), WORK(*)




   F95 INTERFACE
       SUBROUTINE TZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)

       INTEGER :: M, N, LDA, LWORK, INFO
       REAL, DIMENSION(:) :: TAU, WORK
       REAL, DIMENSION(:,:) :: A

       SUBROUTINE TZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)

       INTEGER(8) :: M, N, LDA, LWORK, INFO
       REAL, DIMENSION(:) :: TAU, WORK
       REAL, DIMENSION(:,:) :: A




   C INTERFACE
       #include <sunperf.h>

       void stzrzf(int m, int n, float *a, int lda, float *tau, int *info);

       void stzrzf_64(long m, long n, float *a, long  lda,  float  *tau,  long
                 *info);



PURPOSE
       stzrzf  reduces  the M-by-N ( M<=N ) real upper trapezoidal matrix A to
       upper triangular form by means of orthogonal transformations.

       The upper trapezoidal matrix A is factored as

          A = ( R  0 ) * Z,

       where Z is an N-by-N orthogonal matrix and R is an M-by-M upper  trian-
       gular matrix.


ARGUMENTS
       M (input) The number of rows of the matrix A.  M >= 0.


       N (input) The number of columns of the matrix A.  N >= 0.


       A (input/output)
                 On  entry,  the  leading M-by-N upper trapezoidal part of the
                 array A must contain the matrix to be factorized.   On  exit,
                 the  leading  M-by-M  upper triangular part of A contains the
                 upper triangular matrix R, and elements M+1 to N of the first
                 M  rows  of  A,  with the array TAU, represent the orthogonal
                 matrix Z as a product of M elementary reflectors.


       LDA (input)
                 The leading dimension of the array A.  LDA >= max(1,M).


       TAU (output)
                 The scalar factors of the elementary reflectors.


       WORK (workspace)
                 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


       LWORK (input)
                 The dimension of the array WORK.   LWORK  >=  max(1,M).   For
                 optimum  performance  LWORK  >= M*NB, where NB is the optimal
                 blocksize.

                 If LWORK = -1, then a workspace query is assumed; the routine
                 only  calculates  the optimal size of the WORK array, returns
                 this value as the first entry of the WORK array, and no error
                 message related to LWORK is issued by XERBLA.


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value


FURTHER DETAILS
       Based on contributions by
         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       The N-by-N matrix Z can be computed by

          Z =  Z(1)*Z(2)* ... *Z(M)

       where each N-by-N Z(k) is given by

          Z(k) = I - tau(k)*v(k)*v(k)**T

       with v(k) is the kth row vector of the M-by-N matrix

          V = ( I   A(:,M+1:N) )

       I  is  the M-by-M identity matrix, A(:,M+1:N) is the output stored in A
       on exit from STZRZF, and tau(k) is the kth element of the array TAU.




                                  7 Nov 2015                        stzrzf(3P)